Fermi’s Golden Rule and the Scattering of a Quantum Particle as a Distribution of Matter

Abstract

We calculate the scattering rate of a quantum particle, based on Fermi’s golden rule for a quantum particle as a distribution of matter, where the density of states is a function of the particle Lagrangian, not of the Hamiltonian, as in the conventional theory based on the Schrödinger equation. Thus, the density of states does not refer to the energies as in the conventional form, but to the Lagrangian functions, which, besides the energies, include the momentum-velocity products, that are also constants of motion for the initial and the final states.   We obtain the relativistic dependence on the momentum, and the two scattering rates for the two possible cases, with the spin conservation, or the spin inversion.